After Lyon and Internazionale, it might have felt as though Tottenham Hotspur had wrung every last drop of drama from their involvement in the Europa League's knockout phase. As it turned out, the nerve-shredding victories were only the prelude.

Adversity looked like the default setting for André Villas-Boas and his players on a night of driving rain and pulsating emotion. Never mind the injury absences of Gareth Bale, Aaron Lennon and Jermain Defoe, the team's attacking trident, they had to play extra-time with ten men after the 90th-minute dismissal of Jan Vertonghen for a last-man foul on Marco Streller. The substitute Tom Huddlestone dropped back as an emergency centre-half while another substitute, the rookie Tom Carroll, emerged with honours in midfield.

Tottenham's courage was stirring. They refused to accept that they were beaten in normal time, when they had trailed for the majority of the second half, and Clint Dempsey's late equaliser, his second goal of the night, was a symphony of technique and composure.

The Basel midfielder Mohamed Elneny hit the outside of the post in the first period of extra-time and, in the second, the substitute Alex Frei spurned a glorious chance to win it only for Brad Friedel to block. The pressure was stifling yet Tottenham clung on.

It did not last into the penalty shootout, when Huddlestone and Emmanuel Adebayor missed and Tottenham got that familiar sinking feeling from 12 yards. They have not won a shootout since January 1994, when they beat Peterborough in an FA Cup third round replay, and this would be the seventh consecutive occasion that they had endured agony from the spot.

Tottenham's takers had to contend with ear-splitting shrieks from the vibrant Basel crowd and only Gylfi Sigurdsson could cope. Huddlestone's kick did not make it to the corner, as Yann Sommer dived to save, while Adebayor's was lifted over the crossbar. It is easy to say now but he did not look like scoring and, after the Basel substitute Marcelo Díaz had sparked delirium and blazing flares with his team's fourth conversion, Adebayor was the first Tottenham player off down the tunnel.

The players who went to the travelling fans to give them their shirts were the captain Michael Dawson, Lewis Holtby and Carroll. They had been lion-hearted but there were others who did not deserve the cruel denouement, not least Dempsey, who had put Tottenham in front for the only time over the two legs.

Defensive aberrations pockmarked the evening and Dempsey profited from the first, when Fabian Schär misjudged his sliding challenge as he attempted to cut out Vertonghen's low ball forward. Schär succeeded only in teeing up Dempsey who, with Sommer committed, kept his composure to round the goalkeeper and roll home with his left-foot.

Tottenham's lead did not last. Mousa Dembélé, who started brightly but faded fast, erred with a loose square pass that saw Basel spring forward. Streller ushered in Mohamed Salah, whose desire to unload quickly and without backlift made for a toe-poked effort. It was highly effective, with Friedel beaten low to his left.

After an edgy start on a pitch that did not stand up to the elements, the game crackled to life. Salah was the evening's most impressive performer. His touch, balance and penetration make him a joy to watch and he almost tiptoed through after his goal while Kyle Naughton was booked for pulling him back. Dembélé forced Sommer into a flying 36th-minute save and the second half kicked off to knife-edged tension.

Tottenham were breached, though, from a set-piece and, if the first concession had felt avoidable, there was a grisly undercurrent when they went behind. From Valentin Stocker's near-post corner, Schär flicked on in front of a pack of white shirts and Friedel could do no more than pat the ball out to Aleksander Dragovic, who scored from close range. There are one or two mountains in this country and Tottenham had another one to scale.

The tie might have been over in the 58th minute when Dragovic's towering header from a free-kick had Friedel rooted. All eyes watched for the corner of the net to swell only for the ball to drift wide.

Tottenham dug deep. Spurred by the memories of Dembélé's last-gasp winner in Lyon and the extra-time passage in Milan, courtesy of Adebayor's goal, they continued to believe.

Basel could almost touch their first ever European semi-final and they sought to protect what they had and punch on the counter. But after Dawson's header from Sigurdsson's corner had drawn a reflex save out of Sommer, Tottenham sculpted their lifeline.

Huddlestone's raking crossfield pass exposed Basel and, with the game almost up for Tottenham, Dempsey took an assured touch with his chest and finished with a devastating stab of his left boot. Villas-Boas leapt with delight on the touchline.

The goal fired the drama and after Streller and Kyle Walker had gone close, Vertonghen clipped the Basel striker to see the inevitable flash of red. Tottenham were unbowed against the 11 men but they were unhinged by the penalties. The focus will now turn to the Premier League and the quest to qualify for the Champions League. Broken hearts must be mended.